37.5
9/24=0.375
Move the decimal two places and you get 37.5%
Nah fam math hard math can solve its own problems 82773919
Looks like we're given
![\vec F(x,y)=\langle-x,-y\rangle](https://tex.z-dn.net/?f=%5Cvec%20F%28x%2Cy%29%3D%5Clangle-x%2C-y%5Crangle)
which in three dimensions could be expressed as
![\vec F(x,y)=\langle-x,-y,0\rangle](https://tex.z-dn.net/?f=%5Cvec%20F%28x%2Cy%29%3D%5Clangle-x%2C-y%2C0%5Crangle)
and this has curl
![\mathrm{curl}\vec F=\langle0_y-(-y)_z,-(0_x-(-x)_z),(-y)_x-(-x)_y\rangle=\langle0,0,0\rangle](https://tex.z-dn.net/?f=%5Cmathrm%7Bcurl%7D%5Cvec%20F%3D%5Clangle0_y-%28-y%29_z%2C-%280_x-%28-x%29_z%29%2C%28-y%29_x-%28-x%29_y%5Crangle%3D%5Clangle0%2C0%2C0%5Crangle)
which confirms the two-dimensional curl is 0.
It also looks like the region
is the disk
. Green's theorem says the integral of
along the boundary of
is equal to the integral of the two-dimensional curl of
over the interior of
:
![\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\iint_R\mathrm{curl}\vec F\,\mathrm dA](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B%5Cpartial%20R%7D%5Cvec%20F%5Ccdot%5Cmathrm%20d%5Cvec%20r%3D%5Ciint_R%5Cmathrm%7Bcurl%7D%5Cvec%20F%5C%2C%5Cmathrm%20dA)
which we know to be 0, since the curl itself is 0. To verify this, we can parameterize the boundary of
by
![\vec r(t)=\langle\sqrt5\cos t,\sqrt5\sin t\rangle\implies\vec r'(t)=\langle-\sqrt5\sin t,\sqrt5\cos t\rangle](https://tex.z-dn.net/?f=%5Cvec%20r%28t%29%3D%5Clangle%5Csqrt5%5Ccos%20t%2C%5Csqrt5%5Csin%20t%5Crangle%5Cimplies%5Cvec%20r%27%28t%29%3D%5Clangle-%5Csqrt5%5Csin%20t%2C%5Csqrt5%5Ccos%20t%5Crangle)
![\implies\mathrm d\vec r=\vec r'(t)\,\mathrm dt=\sqrt5\langle-\sin t,\cos t\rangle\,\mathrm dt](https://tex.z-dn.net/?f=%5Cimplies%5Cmathrm%20d%5Cvec%20r%3D%5Cvec%20r%27%28t%29%5C%2C%5Cmathrm%20dt%3D%5Csqrt5%5Clangle-%5Csin%20t%2C%5Ccos%20t%5Crangle%5C%2C%5Cmathrm%20dt)
with
. Then
![\displaystyle\int_{\partial R}\vec F\cdot\mathrm d\vec r=\int_0^{2\pi}\langle-\sqrt5\cos t,-\sqrt5\sin t\rangle\cdot\langle-\sqrt5\sin t,\sqrt5\cos t\rangle\,\mathrm dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_%7B%5Cpartial%20R%7D%5Cvec%20F%5Ccdot%5Cmathrm%20d%5Cvec%20r%3D%5Cint_0%5E%7B2%5Cpi%7D%5Clangle-%5Csqrt5%5Ccos%20t%2C-%5Csqrt5%5Csin%20t%5Crangle%5Ccdot%5Clangle-%5Csqrt5%5Csin%20t%2C%5Csqrt5%5Ccos%20t%5Crangle%5C%2C%5Cmathrm%20dt)
![=\displaystyle5\int_0^{2\pi}(\sin t\cos t-\sin t\cos t)\,\mathrm dt=0](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle5%5Cint_0%5E%7B2%5Cpi%7D%28%5Csin%20t%5Ccos%20t-%5Csin%20t%5Ccos%20t%29%5C%2C%5Cmathrm%20dt%3D0)
Answer:
tree sampling: 2 1/4ft
through 1 year grown: 1 1/6ft
after two years growing: 5ft
1 1/6 coverted into a decimal is 0.16
0.16 x 32 = 5.12 (5)
not sure if this is right, but hope it helps